Three randomly chosen Colorado students were asked how many times they went rock climbing last month. Their replies were 5, 6, 7. The coefficient of variation is:
A)16.7 percent.
B)13.6 percent.
C)20.0 percent.
D)35.7 percent.

Question

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated as the standard deviation (σ) divided by the mean (μ) and is often expressed as a percentage. For the given data (5, 6, 7), the mean (μ) is (5+6+7)/3 = 18/3 = 6. The standard deviation (σ) is calculated using the formula for a sample standard deviation, which is the square root of the sum of squared differences from the mean divided by the number of observations minus one (n-1). Thus, σ = sqrt[((5-6)^2 + (6-6)^2 + (7-6)^2) / (3-1)] = sqrt[(1+0+1)/2] = sqrt(1) = 1. The coefficient of variation is then (σ/μ)*100 = (1/6)*100 = 16.7%.

Three Randomly Chosen Colorado Students Were Asked How Many Times